1
|
Optimal Test Plan of Step-Stress Model of Alpha Power Weibull Lifetimes under Progressively Type-II Censored Samples. Symmetry (Basel) 2022. [DOI: 10.3390/sym14091801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
In this study, the estimation of the unknown parameters of an alpha power Weibull (APW) distribution using the concept of an optimal strategy for the step-stress accelerated life testing (SSALT) is investigated from both classical and Bayesian viewpoints. We used progressive type-II censoring and accelerated life testing to reduce testing time and costs, and we used a cumulative exposure model to examine the impact of various stress levels. A log-linear relation between the scale parameter of the APW distribution and the stress model has been proposed. Maximum likelihood estimators for model parameters, as well as approximation and bootstrap confidence intervals (CIs), were calculated. Bayesian estimation of the parameter model was obtained under symmetric and asymmetric loss functions. An optimal test plan was created under typical operating conditions by minimizing the asymptotic variance (AV) of the percentile life. The simulation study is discussed to demonstrate the model’s optimality. In addition, real-world data are evaluated to demonstrate the model’s versatility.
Collapse
|
2
|
Darzi FH, Mahabadi SE, Haghighi F. Type-II progressive censoring with GLM-based random removal mechanism dependent on the experimental conditions. J Appl Stat 2022; 50:3199-3228. [PMID: 37969896 PMCID: PMC10637206 DOI: 10.1080/02664763.2022.2104230] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2021] [Accepted: 07/15/2022] [Indexed: 10/15/2022]
Abstract
This article presents a novel stochastic removal mechanism under Type-II progressive random censoring in which removal probabilities are allowed to be dependent on the lifetime conditions through Generalized Linear Models (GLM). These conditions potentially include failure distances (the time required to observe the next failure) or other covariate information available in the experiment. The proposed GLM-based random removal mechanism includes a set of tuning parameters that are determined by the researcher according to the possible failure distance category. These parameters allow flexible determination of the removal probabilities leading to necessary experimental cost and time reductions. To establish the proposed mechanism, the Proportional Hazard Rate (PHR) family of distributions is considered. Also, the maximum likelihood estimators of parameters and their asymptotic variances are derived for the Weibull distributed lifetime data. A simple simulation algorithm for generating Type-II progressive censoring samples with GLM-based dependent removal probabilities is also presented. The expected experiment time required to complete the life test under this censoring scheme is also investigated using the Monte Carlo integration method. Several simulation studies are conducted to evaluate and compare the performance of the proposed mechanism. A sensitivity analysis is also considered to study the effect of misspecification of removal mechanism coefficients. Finally, two real data sets are analyzed for illustrative purposes.
Collapse
Affiliation(s)
- Fatemeh Hassantabar Darzi
- School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran
| | - Samaneh Eftekhari Mahabadi
- School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran
| | - Firoozeh Haghighi
- School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran
| |
Collapse
|
3
|
Optimal Plan of Multi-Stress–Strength Reliability Bayesian and Non-Bayesian Methods for the Alpha Power Exponential Model Using Progressive First Failure. Symmetry (Basel) 2022. [DOI: 10.3390/sym14071306] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
It is extremely frequent for systems to fail in their demanding operating environments in many real-world contexts. When systems reach their lowest, highest, or both extreme operating conditions, they usually fail to perform their intended functions, which is something that researchers pay little attention to. The goal of this paper is to develop inference for multi-reliability using unit alpha power exponential distributions for stress–strength variables based on the progressive first failure. As a result, the problem of estimating the stress–strength function R, where X, Y, and Z come from three separate alpha power exponential distributions, is addressed in this paper. The conventional methods, such as maximum likelihood for point estimation, Bayesian and asymptotic confidence, boot-p, and boot-t methods for interval estimation, are also examined. Various confidence intervals have been obtained. Monte Carlo simulations and real-world application examples are used to evaluate and compare the performance of the various proposed estimators.
Collapse
|
4
|
Bhattacharya R, Balakrishnan N. A MCMC-type simple probabilistic approach for determining optimal progressive censoring schemes. COMMUN STAT-SIMUL C 2022. [DOI: 10.1080/03610918.2022.2057537] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Affiliation(s)
- Ritwik Bhattacharya
- Department of Industrial Engineering, School of Engineering and Sciences, Instituto Tecnologico y de Estudios Superiores de Monterrey, Monterrey, México
| | | |
Collapse
|
5
|
Lodhi C, Tripathi YM, Bhattacharya R. On a progressively censored competing risks data from Gompertz distribution. COMMUN STAT-SIMUL C 2021. [DOI: 10.1080/03610918.2021.1879141] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Chandrakant Lodhi
- Department of Mathematics, Indian Institute of Technology Patna, Bihta, India
| | | | - Ritwik Bhattacharya
- Department of Industrial Engineering, School of Engineering and Sciences, Tecnológico de Monterrey, Querétaro, México
| |
Collapse
|
6
|
Mishra N. Optimal one-step censoring schemes under entropy criterion. COMMUN STAT-SIMUL C 2020. [DOI: 10.1080/03610918.2018.1511804] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Nutan Mishra
- Department of Mathematics and Statistics, University of South Alabama, Mobile, Alabama, USA
| |
Collapse
|
7
|
|
8
|
Pérez-González CJ, Fernández AJ. Accurate computation of single and product moments of order statistics under progressive censoring. J STAT COMPUT SIM 2019. [DOI: 10.1080/00949655.2019.1624749] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- Carlos J. Pérez-González
- Departamento de Matemáticas, Estadística e Investigación Operativa, Universidad de La Laguna, La Laguna, Spain
| | - Arturo J. Fernández
- Departamento de Matemáticas, Estadística e Investigación Operativa, Universidad de La Laguna, La Laguna, Spain
| |
Collapse
|
9
|
Bhattacharya R, Saha BN, Farías GG, Balakrishnan N. Multi-criteria-based optimal life-testing plans under hybrid censoring scheme. TEST-SPAIN 2019. [DOI: 10.1007/s11749-019-00660-8] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
|
10
|
Sen T, Pradhan B, Tripathi YM, Bhattacharya R. Fisher information in generalized progressive hybrid-censored data. STATISTICS-ABINGDON 2018. [DOI: 10.1080/02331888.2018.1483934] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/14/2022]
Affiliation(s)
- Tanmay Sen
- Department of Mathematics, Indian Institute of Technology Patna, Patna, India
| | | | | | | |
Collapse
|
11
|
On optimum life-testing plans under Type-II progressive censoring scheme using variable neighborhood search algorithm. TEST-SPAIN 2015. [DOI: 10.1007/s11749-015-0449-z] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
|
12
|
Pradhan B, Kundu D. Inference and optimal censoring schemes for progressively censored Birnbaum–Saunders distribution. J Stat Plan Inference 2013. [DOI: 10.1016/j.jspi.2012.11.007] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
|
13
|
Dahmen K, Burkschat M, Cramer E. A- and D-optimal progressive Type-II censoring designs based on Fisher information. J STAT COMPUT SIM 2012. [DOI: 10.1080/00949655.2011.560118] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
|
14
|
Park S, Ng HKT. Missing information and an optimal one-step plan in a Type II progressive censoring scheme. Stat Probab Lett 2012. [DOI: 10.1016/j.spl.2011.10.012] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
|
15
|
|
16
|
Cramer E, Bagh C. Minimum and Maximum Information Censoring Plans in Progressive Censoring. COMMUN STAT-THEOR M 2011. [DOI: 10.1080/03610926.2010.489176] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
|
17
|
|
18
|
|
19
|
|
20
|
|
21
|
|
22
|
|
23
|
Comments on: Progressive censoring methodology: an appraisal. TEST-SPAIN 2007. [DOI: 10.1007/s11749-007-0066-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
|